×

A Bayesian semiparametric approach for incorporating longitudinal information on exposure history for inference in case-control studies. (English) Zbl 1251.62039

Summary: In a typical case-control study, exposure information is collected at a single time point for the cases and controls. However, case-control studies are often embedded in existing cohort studies containing a wealth of longitudinal exposure history about the participants. Recent medical studies have indicated that incorporating past exposure history, or a constructed summary measure of cumulative exposure derived from the past exposure history, when available, may lead to more precise and clinically meaningful estimates of the disease risk. We propose a flexible Bayesian semiparametric approach to model the longitudinal exposure profiles of the cases and controls and then use measures of cumulative exposure based on a weighted integral of this trajectory in the final disease risk model. The estimation is done via a joint likelihood. In the construction of the cumulative exposure summary, we introduce an influence function, a smooth function of time to characterize the association pattern of the exposure profile on the disease status with different time windows potentially having differential influence/weights. This enables us to analyze how the present disease status of a subject is influenced by his/her past exposure history conditional on the current ones. The joint likelihood formulation allows us to properly account for uncertainties associated with both stages of the estimation process in an integrated manner. Analysis is carried out in a hierarchical Bayesian framework using reversible jump Markov chain Monte Carlo algorithms. The proposed methodology is motivated by, and applied to a case-control study of prostate cancer where longitudinal biomarker information is available for the cases and controls.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
92C50 Medical applications (general)
62N02 Estimation in survival analysis and censored data
62G05 Nonparametric estimation
62F15 Bayesian inference
65C40 Numerical analysis or methods applied to Markov chains
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Albert, Bayesian analysis of binary and polychotomous response data, Journal of the American Statistical Association 88 pp 669– (1993) · Zbl 0774.62031
[2] Botts, A flexible approach to Bayesian curve fitting, Computational Statistics and Data Analysis 52 pp 5100– (2008) · Zbl 1452.62035
[3] Breslow, Statistics in epidemiology: The case control study, Journal of American Statistical Association 91 pp 14– (1996) · Zbl 0870.62082
[4] Breslow, Estimation of multiple relative risk functions in matched case-control studies, American Journal of Epidemiology 108 pp 299– (1978)
[5] Cornfield, A method of estimating comparative rates from clinical data: Applications to cancer of the lung, breast, and cervix, Journal of the National Cancer Institute 11 pp 1269– (1951)
[6] Corneld, Quantal response curves for experimentally uncontrolled variables, Bulletin of the International Statistical Institute 38 pp 97– (1961)
[7] DiMatteo, Bayesian curve fitting with free knot splines, Biometrika 88 pp 1055– (2001) · Zbl 0986.62026
[8] Ernster, Nested case control studies, Preventive Medicine 23 pp 587– (1994)
[9] Essebag, Comparison of nested case-control and survival analysis methodologies for analysis of time-dependent exposure, BMC Medical Research Methodology (2005)
[10] Etzioni, Incorporating the time dimension in receiver operating characteristic curves: A case study of prostate cancer, Medical Decision Making 19 pp 242– (1999)
[11] Freedman, Using time dependent covariate analysis to elucidate the relation of smoking history to Warthin’s tumor risk, American Journal of Epidemiology 170 pp 1178– (2009)
[12] Green, Reversible jump Markov chain Monte Carlo computation and Bayesian model determination, Biometrika 82 pp 711– (1995) · Zbl 0861.62023
[13] Lewis, The increased risk of venous thromboembolism and the use of third generation progestagens: Role of bias in observational research, Contraception 54 pp 5– (1996)
[14] Lindstrom, Penalized estimation of free knot splines, Journal of Computational and Graphical Statistics 8 pp 333– (1999)
[15] Liu, The collapsed Gibbs sampler in Bayesian computations with applications to a gene regulation problem, Journal of the American Statistical Association 89 pp 958– (1994) · Zbl 0804.62033
[16] Lubin, Biased selection of controls for case-control analyses of cohort studies, Biometrics 40 pp 63– (1984)
[17] Mantel, Statistical aspects of the analysis of data from retrospective studies of disease, Journal of the National Cancer Institute 22 pp 719– (1959)
[18] Moulton, Latency and time-dependent exposure in a case-control study, Journal of Clinical Epidemiology 44 pp 915– (1991)
[19] Park, Analysis of longitudinal data in case control studies, Biometrika 91 pp 321– (2004) · Zbl 1079.62120
[20] Prentice, Retrospective studies and failure time models, Biometrika 65 pp 153– (1978) · Zbl 0377.92014
[21] Prentice, Logistic disease incidence models and case-control studies, Biometrika 66 pp 403– (1979) · Zbl 0428.62078
[22] Rice, Equivalence between conditional and random-effects likelihoods for pair-matched case-control studies, Journal of the American Statistical Association 103 pp 385– (2008) · Zbl 1469.62377
[23] Samuelson, Pseudolikelihood approach to analysis of nested case-control studies, Biometrika 84 pp 379– (1997) · Zbl 0882.62107
[24] Seaman, Bayesian analysis of case-control studies with categorical covariates, Biometrika 88 pp 1073– (2001) · Zbl 0986.62095
[25] Seaman, Equivalence of prospective and retrospective models in the Bayesian analysis of case-control studies, Biometrika 91 pp 15– (2004) · Zbl 1132.62364
[26] Thomas, Statistical methods for analyzing effects of temporal patterns of exposure on cancer risks, Scandinavian Journal of Work, Environment and Health 9 pp 353– (1983)
[27] Thomas, Models for exposure-time-response relationships with applications to cancer epidemiology, Annual Review of Public Health 9 pp 451– (1988)
[28] Zelen, Case-control studies and Bayesian inference, Statistics in Medicine 5 pp 261– (1986) · Zbl 0884.62037
[29] Zhang, Two stage functional mixed models for evaluating the effect of longitudinal covariate profiles on a scalar outcome, Biometrics 63 pp 351– (2007) · Zbl 1147.62391
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.